Confusion with Friction and mechanical energy

[DunWorry]

Homework Statement

A sphere rolls from rest down a slope without slipping. Show using energy considerations that the speed of the sphere once it reaches the bottom is V = \sqrt{\frac{10gh}{7}}

Homework Equations

mgh = \frac{1}{2}mv^{2} + \frac{1}{2}Iw^{2}

The Attempt at a Solution

So I managed to do the question, but I did it using energy conservation as shown above. However I was confused as I thought if it rolls without slipping, then friction must be present. If friction is present then the energy conservation should be E_{Initial} = E_{final} + work done by friction. I.e the mechanical energy is not conserved

So shouldn't the equation I used above be mgh = \frac{1}{2}mv^{2} + \frac{1}{2}Iw^{2} + work done by friction?

 

[Doc Al]

For it to roll without slipping, friction does need to be present. But does that friction do any work? What kind of friction is it?

 

[DunWorry]

For it to roll without slipping, friction does need to be present. But does that friction do any work? What kind of friction is it?

Friction does need to be present otherwise it would just slide down the slope?

 

[Doc Al]

Friction does need to be present otherwise it would just slide down the slope?

Right. But is that kinetic or static friction?

 

[MrWarlock616]

You didn't answer his question..

 

[Doc Al]

You didn't answer his question..

Who didn't answer what question?

 

[DunWorry]

Right. But is that kinetic or static friction?

It says A uniform sphere of radius r is released from rest at the top of a slope. Explain whether the mechanical energy is conserved if the sphere A) rolls without slipping down, B) the sphere slides down the slope.

I said if it rolls without slipping then friction must be present (must be kinetic friction then) and then mechanical energy is not conserved. It the sphere slides down the slope then friction is not present (surely static and kinetic friction must not be present?) and mechanical energy is conserved.

 

[Doc Al]

I said if it rolls without slipping then friction must be present (must be kinetic friction then) and then mechanical energy is not conserved.

Half right. Friction must be present, but remember that the sphere rolls without slipping--which means there is no relative movement between the point of contact of the sphere and the surface. So can it be kinetic friction, which is when surfaces slide with respect to each other?

It the sphere slides down the slope then friction is not present (surely static and kinetic friction must not be present?) and mechanical energy is conserved.

That's certainly true.

 

[MrWarlock616]

Sorry Doc Al I posted a little late.. I meant DunWorry didn't answer your question.

When the sphere rolls without slipping, the force of friction is present but it is static. So, it does not do any work.

 

[DunWorry]

Hmmm I'm confused as to firstly why its Static friction and not kinetic friction - I thought if this sphere is rolling, kinetic friction is when two surfaces are sliding against each other ie. when one surface is moving relative to the other and sliding across each other. Static frition is the friction which must be overcome to get the object moving. So when the sphere is rolling down this slope, it must be the kinetic friction and not the static friction which is acting.

B)Why if it is static friction no work is done but if it is kinetic friction then work is done

 

[Doc Al]

Hmmm I'm confused as to firstly why its Static friction and not kinetic friction - I thought if this sphere is rolling, kinetic friction is when two surfaces are sliding against each other ie. when one surface is moving relative to the other and sliding across each other.

Exactly! But the surface of the sphere does not slide across the surface--it rolls without slipping.

Static frition is the friction which must be overcome to get the object moving. So when the sphere is rolling down this slope, it must be the kinetic friction and not the static friction which is acting.

What static friction does is prevent the slipping and sliding between the surfaces. The static friction is just what it needs to be to keep the ball rolling without sliding.

B)Why if it is static friction no work is done but if it is kinetic friction then work is done

For a force to do work the point of contact must move through some displacement.

 

[rcgldr]

Hmmm I'm confused as to firstly why its Static friction and not kinetic friction

Static friction is the term used when there is no relative movment (slipping or sliding) between surfaces. So since the sphere is rolling without slipping, it's static friction.

Why if it is static friction no work is done but if it is kinetic friction then work is done

The work done by kinetic friction is equal to the amount of energy converted into heat due to sliding or slipping.

In this case, the force that the plane exerts onto the rolling sphere through static friction increases the sphere's angular kinetic energy and decreases the sphere's gain in linear kinetic energy by the same magnitude, so no net work is done by the force related to static friction (in this case).

For an alternate case, imagine a sphere initially at rest on a very long treadmill surface, and that the treadmill surface begins to accelerate to the right at some constant rate of acceleration. In this case, the force that the treadmill exerts on the sphere through static friction increases the sphere's angular and linear kinetic energies. The work done on the sphere is considered performed by the treadmill, not static friction. It might help to consider that the term static friction applies to both parts of a Newton third law pair of forces, the force the treadmill exerts onto the sphere, and the equal in magnitude but opposing reaction force to acceleration that the sphere exerts onto the treadmill.

For kinetic friction, a simple example would be a force used to slide a box along a surface at constant speed. All of the work done by the force is being converted into heat by kinetic friction, and the box's kinetic energy remains constant.

 

[DunWorry]

I see, I understand now, however what if if the sphere slides down the slope? would mechanical energy be conserved? I thought for it to slide there must be no friction present, so it would be conserved as none would be dissipated, if it rolls without slipping then since it is static friction acting on the bottom of the sphere which is instantaneously stationary mechanical energy is conserved. If the sphere Slips whilst rolling, then that means kinetic friction is present, and energy would be dissipated, can someone check this please?

Thankyou.

 

[Doc Al]

If the sphere Slips whilst rolling, then that means kinetic friction is present, and energy would be dissipated, can someone check this please?

Right. If the sphere slips as it rolls, that means that the static friction was insufficient to prevent slipping. Thus kinetic friction acts and mechanical energy is no longer conserved.